Affirming a disjunct
Encyclopedia
The logical fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a deductive argument takes the following logical form
:
Or in logical operators:
¬ 
Where
denotes a logical assertion
.
.
This inference
is invalid. If Max is a cat then Max is also a mammal. (Remember "or" is defined in an inclusive sense not an exclusive sense.)
The above example of an argument also demonstrates the fallacy.
Logical form
In logic, the logical form of a sentence or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form...
:
- A or B
- A
- Therefore, it is not the case that B
Or in logical operators:
¬ Where
denotes a logical assertionLogical assertion
A logical assertion is a statement that asserts that a certain premise is true, and is useful for statements in proof. It is equivalent to a sequent with an empty antecedent....
.
Explanation
The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true. This results from "or" being defined inclusively rather than exclusively. Affirming the disjunct should not be confused with the valid form known as the disjunctive syllogismDisjunctive syllogism
A disjunctive syllogism, also known as disjunction-elimination and or-elimination , and historically known as modus tollendo ponens,, is a classically valid, simple argument form:where \vdash represents the logical assertion....
.
Example
The following argument indicates the invalidity of affirming a disjunct:- Max is a cat or Max is a mammal.
- Max is a cat.
- Therefore, Max is not a mammal.
This inference
Inference
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...
is invalid. If Max is a cat then Max is also a mammal. (Remember "or" is defined in an inclusive sense not an exclusive sense.)
- The car is red or the car is large.
- The car is red.
- Therefore, the car is not large.
The above example of an argument also demonstrates the fallacy.